1983 AIME Problems/Problem 8
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Problem
What is the largest 2-digit prime factor of the integer 
?
Solution
Expanding the binomial coefficient, we get 
. Let the prime be 
; then 
. If 
, then the factor of appears twice in the denominator. Thus, we need to appear as a factor three times in the numerator, or 
. The largest such prime is 
, which is our answer.
See also
| 1983 AIME (Problems • Resources) | ||
| Preceded by Problem 7 | Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
